Question

5a) A 5-kg object travels at a constant velocity of 25 m/s east on a smooth, frictionless surface. An 8-kg object travels at a constant velocity of 55 m/s west on the same surface and then collides directly with the 5 kg-object. The two objects stick together. What is the velocity of the two-object system, just after they collide and stick together?

b) After a .20 kg street-hockey puck is hit, it has an initial velocity of 35 m/s and travels on a uniform, horizontal cement surface and uniformly slows to a stop in 6 seconds (due to the friction between the puck and the cement). What is the coefficient of kinetic friction between the puck and the cement surface?

c) A horizontal spring has a spring constant of 150 N/m. ; a 0.25 kg mass is placed at the spring's free end, on a level, horizontal, frictionless surface. The spring- mass system is compressed 12 cm, and then released from rest. What is the maximum speed, in meters per second, of the released mass?

Answer 1

5 (a) Let m1 = 5kg travelling with an initial velocity u1 = 25m/s in the east direction and m2 = 8kg travelling with an initial velocity u2 = 55m/s in the west direction. They stick together after the collision. Let v be their velocity after collision. Applying momentum conervation,

Taking east direction as positive and west direction as negative,

So the magnitude of velocity of the system after collision is 24.23m/s and since its value is negative, their direction is towards west.

(b) For arough surface,

Given the initial velocity of the puck is u = 35m/s and the time taken for it to stop is t = 6s. Since it is stopping the final velocity v = 0. Therefore,

So the coefficient of kinetic friction between puck and the cement is 0.59.

(c) Given the spring constant of the spring k = 150N/m, the mass m = 0.25kg and the compression of the spring x = 12cm = 0.12m. Let v be the velocity of the mass. Applying conservation of energy,

So the maximum speed of the released mass is 2.94m/s.